Origin of Scale-Dependent Dispersivity and Its Implications for Miscible Gas Flooding

DE-FC26-03NT15534

Project Goal
The objectives of this project are to perform a novel fundamental study of the mechanism of dispersion, to develop an improved multiscale statistical model of dispersion, and to use this advance in understanding to optimize field-scale displacements.

Performers
University of Texas at Austin, Austin, TX
University of California, Merced, CA

Results
Large-scale high resolution 3D simulation studies show that measuring dispersion in flow reversal tests (also referred to as push-pull tests or echo tests) is the single most powerful technique for establishing the relative contributions of diffusion (mixing at molecular scale) and heterogeneity (the variability of flow speeds on streamlines resulting from natural spatial variability of the permeability of a formation.) If diffusion is small, then a flow reversal experiment shows the dispersion is largely reversible. The time required to reach “vertical equilibrium” depends on the magnitude of diffusion and the correlation length of the permeability field in the primary direction of flow. If diffusion is large, then flow reversal does not reverse the spreading of the tracer front. However the dispersion coefficient, as measured by the variance of the location of tracer particles in the simulations, does not increase during the period of reverse flow.

Transmission and echo dispersivities were estimated for a wide range of reservoir descriptions (varying heterogeneity, correlation lengths and anisotropy). The simulated data fall within the overall trend of the dispersivity-length plot (Gelhar et al., 1992). High values of echo dispersivities (up to 10m) which are comparable to the corresponding transmission value indicate significant levels of mixing occurring in such displacements. The magnitude of the echo dispersivity and the nature of the mixing zone growth are largely dependent on the correlation lengths of the permeability field.

The essential grain-scale phenomena giving rise to hydrodynamic dispersion observed in porous media are (i) stream splitting of the solute front at every pore, thus causing independence of particle velocities purely by convection, (ii) a velocity gradient within throats and (iii) diffusion. Taylor’s dispersion in a capillary tube accounts for only the second and third of these phenomena, yielding a quadratic dependence of dispersion on Peclet number. Plug flow in the bonds of a physically representative network accounts for the only the first and third phenomena, resulting in a linear dependence of dispersion upon Peclet number.

Benefits
This project is developing improved models and simulators to establish a better grasp of the parameters that control optimal performance in miscible and near-miscible displacements. This capability will also enable better translation of laboratory results to field projects.

Background
The ultimate oil recovery efficiency from carbon dioxide (CO2) injection is low. The CO2 utilization rate—the amount of CO2 injected to recover a barrel of oil—is high. The performance of a CO2 process is strongly influenced by hydrodynamic dispersion, but the appropriate level of dispersivity to use at the scale of reservoir simulation is largely unknown. That dispersivity increases with scale (travel distance) has been known for more than 30 years. There is substantial ambiguity about what causes the scale dependence. Part of the work being proposed here is to investigate the scale dependence downward—from the core or column scale to the pore scale—as opposed to upward, as has been done previously. This approach has never been tried as part of an effort to understand the fundamental mechanism of dispersion.

Summary
The most striking accomplishment of this project was the solution of a long-standing problem in transport through porous media, namely, the determination of the pore-scale origin of macroscopic hydrodynamic dispersion. Using a physically representative network model of a simple but geometrically realistic porous medium, the researchers developed the first algorithm for completely reversible (no diffusion) particle motion at network junctions. This enabled the first analysis of the contribution of convective spreading at the pore-scale. With this model, the researchers demonstrated that the combination of flow splitting (as fluid enters a pore then goes around grains), parabolic velocity profiles within pore throats (due to viscous momentum transfer to pore walls) and diffusion within pore throats (enabling particle to sample different streamlines within a throat) are necessary and sufficient to explain (predict without adjustable parameters) the long-standing observation that dispersion coefficient scales nonlinearly (the power-law exponent is 1.2) with pore-scale Peclet number.

The project researchers also:

Developed a PVC-based fabrication technique for creating cost-effective nitrate sensors to better support transport studies in porous media

Demonstrated the utility of particle tracking simulations of flow reversal (echo) tests to identify the nature of transport.

Demonstrated the possibility of significant levels of mixing occurring in field scale miscible displacements for typical reservoir heterogeneity conditions.

Harmon, T.C., Jursich, N.L., Davidson, M.J., and Haux, J.E., Scaleable Nitrate Microsensors in the Form of a Plant Root, fall meeting of the American Geophysical Union, December 13-17, 2004, San Francisco, CA.

The figure shows dispersion coefficient obtained using direct simulation of particle tracking in a physically representative network model of porous media. The simulated results match well with the experimental data available in the literature

Above left is the evolution of the longitudinal dispersivity (estimated from high resolution particle tracking simulations) with distance travelled for three cases with increasing correlation lengths. Both transmission (dots) and echo dispersivities (squares) increase to values much greater than core scale (input) values. The nature of mixing zone growth also changes from almost fickian for the short correlation cases to non-fickian for the long correlation length case.

Shown above are flow-through experiment results for triplicate PVC-based nitrate sensors each receiving a series of six 50 ppm nitrate spikes; the results indicated only a modest drift in sensor calibration over the three-day period.

Above left is a computer generated dense packing of spheres, which serves as a model sediment like those used for pore-scale dispersion measurements reported previously in this project. Above right is result of direct simulation of particle tracking within the pore space of this packing, using a physically representative network to compute the flow field. The results are consistent with experimental observations and will be the basis for examining the role of diffusion at this scale.